Crime and punishment: Does it pay to punish?

► According to Becker: crime is committed if utility is positive. ► Different from Becker we consider also an honesty idiosyncratic factor. ► Sharp discontinuous decrease in criminality is observed for a critical value of the probability of punishment. ► A hysteresis is observed when this probability changes in time. ► Hysteresis indicates that is harder to recover from a high criminality situation.